Chapter 1.

1.1 Problem Statement

{2,4,5,6,7,8}
$b+1
round(sqrt($a*$a+$b*$b),2)
round($b/$c,2)
round($a/$c,2)
round($c/$a,2)
round($a/$b,2)

Assume that . Find sin(θ), sec(θ), and cot(θ) if tan(θ)=.

1.2 Step 1

Recall the signs of sin(θ) and cos(θ) for .

Question Sequence

Question 1.1

For , sin(θ) and cos(θ) are AHS/KvCvN60M0alrhEg6js74p/c5bldxDkt6KSfGLDzGp0rD. Thus we can use the definitions of the trigonometric functions associated with a right triangle to find sin(θ), sec(θ), and cot(θ).

Incorrect
Correct

1.3 Step 2

Draw a right triangle to find sin(θ) and cos(θ) given that tan(θ)=.

Label θ as one of the acute angles inside the right triangle. Label the leg of the triangle opposite θ as b and label the leg of the triangle adjacent to θ as a. Label the hypotenuse c.

According to this triangle, we can solve for b and a using the relationship

.

Question Sequence

Question 1.2

Since , we have b = $b and a = nc1ItEz0kR4=.

Incorrect
Correct

Question 1.3

We can find c using the Pythagorean theorem, which states that the sum of the squares of the legs of a right triangle equals the square of the hypotenuse.

a2 + b2 = c2

c = SFgqQUkJGdg=

(Rounded to two decimal places.)

Incorrect
Correct

1.4 Step 3

Knowing that a = $a, b = $b, and c = $c, we can solve for sin(θ) and cos(θ) using their definitions with respect to a right triangle.

Question Sequence

Question 1.4

= 6Dfm+jOF/bgyzWF+wDvdrAfl09QnFwc2BQzoCQ==.

2
Correct.
Incorrect.

Question 1.5

=/FbchM+7zRJiP0bzLMC4Y9L2TVmxGBe8cM/k6w==.

Correct.
Incorrect.

Question 1.6

For and tan(θ)=,

sin(θ) = SSlBS8LbM0I=

and

cos(θ) = xn/8UFOXYhs=.

(Rounded to two decimal places.)

Correct.
Incorrect.

1.5 Step 4

Recall the definitions of sec(θ) and cot(θ).

Question 1.7

sec(θ) = KiMf4AhgqCQxuq59j8foAV9wxlzjNxxk

cot(θ) = jpYz/8GIrJycRjmEe59p/Kdg32bIgAu5PQbcRRUFZV6siY2w

Correct.
Incorrect.

1.6 Step 5

Find and simplify sec(θ) and cot(θ) using, from Step 3, sin(θ) = $sin and cos(θ) = $cos.

Question Sequence

Question 1.8

For and tan(θ) = we have

sec(θ) = fxYeI31FYsY=

(Rounded to two decimal places.)

Correct.
Incorrect.

Question 1.9

For and tan(θ) = we have

cot(θ) = tE/bvqTBTKc=

(Rounded to two decimal places.)

Correct.
Incorrect.